Unicellularity of the multiplication operator on Banach spaces of formal power series

Volume 147 / 2001

B. Yousefi Studia Mathematica 147 (2001), 201-209 MSC: Primary 47B37; Secondary 47A25. DOI: 10.4064/sm147-3-1

Abstract

Let $\{\beta(n)\}^{\infty}_{n=0}$ be a sequence of positive numbers and $1 \leq p < \infty$. We consider the space $\ell^{p}(\beta)$ of all power series $f(z)\hskip-2pt =\hskip-2pt \sum^{\infty}_{n=0} \skew4\widehat{f}(n)z^{n}$ such that $\sum_{n=0}^{\infty} |\skew4\widehat{f}(n)|^{p}|\beta(n)|^{p} < \infty$. We give some sufficient conditions for the multiplication operator, $M_{z}$, to be unicellular on the Banach space $\ell^{p}(\beta)$. This generalizes the main results obtained by Lu Fang [1].

Authors

  • B. YousefiCollege of Sciences
    Shiraz University
    Shiraz 71454, Iran
    e-mail

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